Question

A report States that the cost of repairing a hybrid vehicle is falling even while typical repairs on conventional vehicles are getting more expensive. The most common hybrid repaired replacing the hybrid Inverter assembly had a mean repair cost of 3927 in 2012. Industry experts suspect that the cause will continue to decrease given the increase in a number of technicians who have gained expertise on fixing gas electric engines in recent months. Suppose a sample of 100 hybrid inverter assembly repairs completed in the last month was selected. The sample mean repair cost was $3780 with a sample standard deviation of $600. Complete parts A and B below.

a. is there evidence that the population mean cost is less than $3,927? (use a 0.05 level of significance)
state the null and alternative hypothesis.

-find the test statistic for this hypothesis test.
(round to two decimal places as needed)

-The critical value for the test statistics is/are...
(round to two decimal places and use commas to separate answers)

b. determine the p-value
(round to three decimal places as needed)

Answer 1

I will use the t distribution here to demonstrate the process of hypothesis testing given the sample statistics above.

Note that the formula for the t - distribution can be calculated as.

The idea is to calculate the test statistic and to compare with the critical value, and the null hypothesis is rejected in the test statistic is more extreme than the critical value.

So culculate

The null hypotheses to be tested are as follows.

H_0: mu greater or equal to 3927
H_1: mu is less than 3927

This is a left-tailed test and so the critical value should be a negative value.

critical value= -1.660

The null hypothesis is rejected because the test statistic is more extreme than the critical value. test statistic above -2.45 is less than -1.660.

The conclusion finds sufficient evidence to support the claim proposed by the experts. that the cost has been decreasing.